Convert the equation \( \rho=8 \) to rectangular coordinates and write in standard form.

To convert the equation \( \rho = 8 \) from polar to rectangular coordinates, we can use the relationship between polar and rectangular coordinates. In polar coordinates, \( \rho \) represents the distance from the origin, and in rectangular coordinates, this distance can be expressed as: \[ \rho = \sqrt{x^2 + y^2} \] Given the equation \( \rho = 8 \), we can substitute this into the equation: \[ \sqrt{x^2 + y^2} = 8 \] Next, we will square both sides to eliminate the square root: \[ x^2 + y^2 = 8^2 \] Calculating \( 8^2 \): \[ x^2 + y^2 = 64 \] This is the equation of a circle in standard form, where the center is at the origin \((0, 0)\) and the radius is \(8\). Thus, the equation \( \rho = 8 \) in rectangular coordinates and standard form is: \[ x^2 + y^2 = 64 \]